Answer :
Sure! Let's multiply [tex]\((x^2 - 5x)\)[/tex] by [tex]\((2x^2 + x - 3)\)[/tex] step-by-step.
1. Distribute the first term of the first expression:
Multiply [tex]\(x^2\)[/tex] by each term in the second expression [tex]\((2x^2 + x - 3)\)[/tex]:
[tex]\[
x^2 \cdot 2x^2 = 2x^4
\][/tex]
[tex]\[
x^2 \cdot x = x^3
\][/tex]
[tex]\[
x^2 \cdot (-3) = -3x^2
\][/tex]
So, the expression becomes: [tex]\(2x^4 + x^3 - 3x^2\)[/tex].
2. Distribute the second term of the first expression:
Multiply [tex]\(-5x\)[/tex] by each term in the second expression [tex]\((2x^2 + x - 3)\)[/tex]:
[tex]\[
-5x \cdot 2x^2 = -10x^3
\][/tex]
[tex]\[
-5x \cdot x = -5x^2
\][/tex]
[tex]\[
-5x \cdot (-3) = 15x
\][/tex]
So, the expression becomes: [tex]\(-10x^3 - 5x^2 + 15x\)[/tex].
3. Combine all the terms:
Add the results of the two distributions together:
[tex]\[
2x^4 + x^3 - 3x^2 - 10x^3 - 5x^2 + 15x
\][/tex]
4. Simplify by combining like terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
The resulting expression is:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
So, the answer is [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex], which corresponds to option B.
1. Distribute the first term of the first expression:
Multiply [tex]\(x^2\)[/tex] by each term in the second expression [tex]\((2x^2 + x - 3)\)[/tex]:
[tex]\[
x^2 \cdot 2x^2 = 2x^4
\][/tex]
[tex]\[
x^2 \cdot x = x^3
\][/tex]
[tex]\[
x^2 \cdot (-3) = -3x^2
\][/tex]
So, the expression becomes: [tex]\(2x^4 + x^3 - 3x^2\)[/tex].
2. Distribute the second term of the first expression:
Multiply [tex]\(-5x\)[/tex] by each term in the second expression [tex]\((2x^2 + x - 3)\)[/tex]:
[tex]\[
-5x \cdot 2x^2 = -10x^3
\][/tex]
[tex]\[
-5x \cdot x = -5x^2
\][/tex]
[tex]\[
-5x \cdot (-3) = 15x
\][/tex]
So, the expression becomes: [tex]\(-10x^3 - 5x^2 + 15x\)[/tex].
3. Combine all the terms:
Add the results of the two distributions together:
[tex]\[
2x^4 + x^3 - 3x^2 - 10x^3 - 5x^2 + 15x
\][/tex]
4. Simplify by combining like terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(x^3 - 10x^3 = -9x^3\)[/tex]
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-3x^2 - 5x^2 = -8x^2\)[/tex]
The resulting expression is:
[tex]\[
2x^4 - 9x^3 - 8x^2 + 15x
\][/tex]
So, the answer is [tex]\(2x^4 - 9x^3 - 8x^2 + 15x\)[/tex], which corresponds to option B.
